Membranes with Fluctuating Topology: Monte Carlo Simulations

Much of the phase behavior observed in self-assembling amphiphilic systems can be understood in the context of ensembles of random surfaces. In this article, it is shown that Monte Carlo simulations of dynamically triangulated surfaces of fluctuating topology can be used to determine the structure and thermal behavior of sponge phases, as well as the sponge-to-lamellar transition in these systems. The effect of the saddle-splay modulus, $\overline{\kappa }$, on the phase behavior is studied systematically for the first time. Our data provide strong evidence for a positive logarithmic renormalization of $\overline{\kappa }$; this result is consistent with the lamellar-to-sponge transition observed in experiments for decreasing amphiphile concentration.